Tanizaki's Computational Methods in Statistics and Econometrics by GAUSS

1. Elements of Statistics

1.1 Event and Probability

1.2 Random Variable and Distribution

1.3 Mathematical Expectation

1.4 Transformof Variables

1.5 Moment-Generating Function

1.6 Law of large Numbers and Central Limit Theorem

1.7 Statistical Inference

1.8 Testing Hypothesis

1.9 Regression Analysis

I. Monte Carlo Statistical Methods

2. Random Number Generation I

2.1 Uniform Distribution: U(0,1)

• urnd16.txt urnd.txt

2.2 Transforming U(0,1): Continuous Type

• snrnd.txt snrnd2.txt snrnd3.txt snprob.txt snperpt.txt nrnd.txt lognrnd.txt

• exprnd.txt gammarnd.txt igammarnd.txt betarnd.txt chi2rnd.txt chi2rnd2.txt chi2rnd3.txt chi2prob.txt chi2perpt.txt

• frnd.txt trnd.txt tprob.txt tperpt.txt dexprnd.txt nchi2rnd.txt nfrnd.txt ntrnd.txt

2.3 Inverse Transform Method

• urnd_ab.txt snrnd4.txt dexprnd2.txt crnd.txt logisticrnd.txt gumbelrnd.txt paretornd.txt wrnd.txt

2.4 Using U(0,1): Discrete Type

• recrnd.txt brnd.txt geornd.txt geornd2.txt pornd.txt pornd2.txt birnd.txt birnd2.txt birnd3.txt

• nbirnd.txt nbirnd2.txt hgeornd.txt hgeornd2.txt

2.5 Multivariate Distribution

• mnrnd.txt mvar.txt

3. Random Number Generation II

3.1 Composition Method

• snrnd5.txt snrnd5_2.txt bimodal.txt multimodal.txt

3.2 Rejection Sampling

• snrnd6.txt gammarnd2.txt gammarnd3.txt

3.3 Importance Resampling

• snrnd7.txt gammarnd4.txt betarnd2.txt

3.4 Metropolis-Hastings Algorithm

• snrnd8.txt gammarnd5.txt betarnd3.txt

3.5 Ratio-of-Uniforms Method

• snrnd9.txt gammarnd6.txt gammarnd7.txt gammarnd8.txt chi2rnd4.txt chi2rnd5.txt chi2rnd6.txt

3.6 Gibbs Sampling

3.7 Comparison of Sampling Methods

II. Selected Applications of Monte Carlo Methods

4. Bayesian Estimation

4.1 Elements of Bayesian Inference

4.2 Heteriscedasticity Model

4.3 Autocorrelation Model

5. Bias Correction of OLSE in AR Models

5.1 Introduction

5.2 OLSE Bias

5.3 Bias Correction Method

5.4 Monte Carlo Experiments

5.5 Empirical Example

6. State Space Modeling

6.1 Introduction

6.2 State Space Models

6.3 Recursive Algorithm

6.4 Non-Recursive Algorithm

6.5 Monte Carlo Studies

6.6 Empirical Example

III. Nonparametric Statistical Methods

7. Difference Between Two-Samoke Means

7.1 Introduction

7.2 Overview of Nonparametric Tests

7.3 Asymptotic Relative Efficiency

7.4 Power Comparison(Small Sample Properties)

7.5 Empirical Example: Testing Structural Changes

8. Independence between Two Samples

8.1 Introduction

8.2 Nonparametric tests in Independence

8.3 Monte Carlo Experiments

8.4 Empirical Example

• Hisashi Tanizaki "Computational Methods in Statistics and Econometrics" Marcel Dekker Inc. 2004 ISBN: 0824748042.

This is a GAUSS version of its "complete" programming guide. Buy and read the textbook above along with this guide.

by Yosuke Amijima

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